Molecular dynamics simulation of diffusion of gases in a carbon-nanotube–polymer composite

Extensive molecular dynamics (MD) simulations were carried out to compute the solubilities and self-diffusivities of $\mathrm{C}{\mathrm{O}}_2$ and $\mathrm{C}{\mathrm{H}}_4$ in amorphous polyetherimide (PEI) and mixed-matrix PEI generated by inserting single-walled carbon nanotubes into the polymer. Atomistic models of PEI and its composites were generated using energy minimizations, MD simulations, and the polymer-consistent force field. Two types of polymer composite were generated by inserting (7,0) and (12,0) zigzag carbon nanotubes into the PEI structure. The morphologies of PEI and its composites were characterized by their densities, radial distribution functions, and the accessible free volumes, which were computed with probe molecules of different sizes. The distributions of the cavity volumes were computed using the Voronoi tessellation method. The computed self-diffusivities of the gases in the polymer composites are much larger than those in pure PEI. We find, however, that the increase is not due to diffusion of the gases through the nanotubes which have smooth energy surfaces and, therefore, provide fast transport paths. Instead, the MD simulations indicate a squeezing effect of the nanotubes on the polymer matrix that changes the composite polymers’ free-volume distributions and makes them more sharply peaked. The presence of nanotubes also creates several cavities with large volumes that give rise to larger diffusivities in the polymer composites. This effect is due to the repulsive interactions between the polymer and the nanotubes. The solubilities of the gases in the polymer composites are also larger than those in pure PEI, hence indicating larger gas permeabilities for mixed-matrix PEI than PEI itself.

Figure 1

(Color online) Repeating units of the PEI (top) structure and the zigzag (7,0) carbon nanotube (bottom).

Figure 2

(Color online) Calculated radial distribution functions of PEI and its composites.

Figure 3

Fluctuations with the time of the accessible free-volume fractions of PEI and its composites. The probe size is $2.5\mathrm{\AA }$.

Figure 4

The distributions of the free-volume fractions of PEI and its composites, averaged over 20 configurations.

Figure 5

Three-dimensional view of the mixed-matrix PEI structure within the simulation cell.

Figure 6

Time evolution of the cavity volume distributions in PEI and its composites.

Figure 7

The distributions of the cavity volumes in PEI and its composites, averaged over 20 realizations.

Figure 8

The excess chemical potentials of $\mathrm{C}{\mathrm{H}}_4$ (circles) and $\mathrm{C}{\mathrm{O}}_2$ (triangles) in the three materials.

Figure 9

The ensemble of the trajectories of $\mathrm{C}{\mathrm{O}}_2$ and $\mathrm{C}{\mathrm{H}}_4$ in the PEI structure.

Figure 10

Same as in Fig. 9, but in the MMP7 structure.

Figure 11

Time dependence of the displacements of $\mathrm{C}{\mathrm{O}}_2$ and $\mathrm{C}{\mathrm{H}}_4$ from their initial positions in the PEI structure.

Figure 12

Same as in Fig. 11, but in the MMP7 structure.

Figure 13

Time dependence of the MSDs of $\mathrm{C}{\mathrm{O}}_2$ in the PEI structure (left) and its logarithmic plot (right), computed using the $\left(NPT\right)$ ensemble.

Figure 14

Same as in Fig. 13, but for $\mathrm{C}{\mathrm{H}}_4$.

Figure 15

Time-dependence of the mean-square displacements of $\mathrm{C}{\mathrm{O}}_2$ and $\mathrm{C}{\mathrm{H}}_4$ in the PEI structure, computed using the $\left(NPT\right)$ ensemble.

Figure 16

Time dependence of the MSDs of the two gases in the polymer composites, computing using the $\left(NVT\right)$ ensemble.